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Simplifying x4 + -14x2 + 15 = 0 Reorder the terms: 15 + -14x2 + x4 = 0 Solving 15 + -14x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -14x2 + -15 + x4 = 0 + -15 Reorder the terms: 15 + -15 + -14x2 + x4 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -14x2 + x4 = 0 + -15 -14x2 + x4 = 0 + -15 Combine like terms: 0 + -15 = -15 -14x2 + x4 = -15 The x term is -14x2. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x2 + 49 + x4 = -15 + 49 Reorder the terms: 49 + -14x2 + x4 = -15 + 49 Combine like terms: -15 + 49 = 34 49 + -14x2 + x4 = 34 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x2 + -7) equal to 5.830951895 and -5.830951895.Subproblem 1
x2 + -7 = 5.830951895 Simplifying x2 + -7 = 5.830951895 Reorder the terms: -7 + x2 = 5.830951895 Solving -7 + x2 = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = 5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 5.830951895 + 7 x2 = 5.830951895 + 7 Combine like terms: 5.830951895 + 7 = 12.830951895 x2 = 12.830951895 Simplifying x2 = 12.830951895 Take the square root of each side: x = {-3.582031811, 3.582031811}Subproblem 2
x2 + -7 = -5.830951895 Simplifying x2 + -7 = -5.830951895 Reorder the terms: -7 + x2 = -5.830951895 Solving -7 + x2 = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x2 = -5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -5.830951895 + 7 x2 = -5.830951895 + 7 Combine like terms: -5.830951895 + 7 = 1.169048105 x2 = 1.169048105 Simplifying x2 = 1.169048105 Take the square root of each side: x = {-1.081225279, 1.081225279}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.582031811, 3.582031811, -1.081225279, 1.081225279}
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